Coursera-Machine Learning-ex5

Some Points:

The Results:

• linearRegCostFunction.m

function [J, grad] = linearRegCostFunction(X, y, theta, lambda)

% Initialize some useful values
m = length(y); % number of training examples

% You need to return the following variables correctly 
J = 0;
grad = zeros(size(theta));

diff = X * theta - y;
regu = lambda * theta(2:end)' * theta(2:end);
J = (diff' * diff + regu) / (2 * m);

grad = (X' * diff + lambda * [0; theta(2:end)]) / m;
grad = grad(:);

end
           

• learningCurve.m

function [error_train, error_val] = ...
    learningCurve(X, y, Xval, yval, lambda)


% Number of training examples
m = size(X, 1);

% You need to return these values correctly
error_train = zeros(m, 1);
error_val   = zeros(m, 1);


for i = 1:m
	theta = trainLinearReg(X(1:i, :), y(1:i), lambda);
	error_train(i) = linearRegCostFunction(X(1:i, :), y(1:i), theta, 0);
	% for the cross validation error,you should compute it over the entire cross validation set.
	error_val(i) = linearRegCostFunction(Xval, yval, theta, 0);
end

end
           

•  validationCurve.m

function [lambda_vec, error_train, error_val] = ...
    validationCurve(X, y, Xval, yval)

% Selected values of lambda (you should not change this)
lambda_vec = [0 0.001 0.003 0.01 0.03 0.1 0.3 1 3 10]';

% You need to return these variables correctly.
error_train = zeros(length(lambda_vec), 1);
error_val = zeros(length(lambda_vec), 1);


for i =1:length(lambda_vec)
	lambda = lambda_vec(i);
	theta = trainLinearReg(X, y, lambda);
	error_train(i) = linearRegCostFunction(X, y, theta, 0);
	error_val(i) = linearRegCostFunction(Xval, yval, theta, 0);
end


end